Question

if alpha and beta are the roots of the equation (x-a)(x-b)=c then show that alpha and beta are the roots of (x-alpha)(x-beta)c=0
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Answer 1

Answer:Given α,β are the roots of (x−a)(x−b)−c=0

⇒(x−a)(x−b)−c=(x−α)(x−β)

⇒(x−a)(x−b)=(x−α)(x−β)+c

⇒a,b are the roots of equation (x−α)(x−β)+c=0